Motion in straight line class 11 physics | Graphs | x-t graphs |Part 4

0:02 [Music] hey everyone welcome to home school and welcome back to class 11 physics series and we are with the chapter motion in a straight line where i have completed all the concepts except one topic that is all about graphs okay say graphs actually makes life quite easier because most of the difficult problems that you feel difficult to calculate using formulas can be calculated easily using graphs okay so to some extent graphs are used to describe about a motion looking at a graph we can come to know

0:47 many many things about emotion right so today we are going to discuss everything about graphs how can we plot a graph when a information is given and from a graph what all the informations that we can take and use it to calculate a problem all that we will discuss definitely video is going to be a very very helpful video and uh you get a kind of confidence after watching this video so don't miss it out watch till the end fine say coming to a graph say everybody ah must have had a basic idea how to plot a graph right so you know uh graph in the sense you will have two axis one is x

1:34 axis y axis with a particular scale you know what with the given information we know how to mark the points and then join the points we may get a straight line or we may get a curved line you know that line whatever the line that you plot that is called as graph and that line or a curve will tell you lots of information okay so here our motion is also very well described by graphs okay so we mainly study about three types of graphs so the first one is position time graph so this is this is a very simple graph but it's a very powerful tool that can

2:21 tell about many many important things okay so we learn a lot of things from this position time graph okay so uh in short we can also call it as xt graph right fine and the second important thing is velocity time graph even this can uh make our things quite easy about solving numericals of acceleration okay so velocity time graph in short we can call it as vt graph right so two graphs are very very important and they can act as a very very powerful tools to solve all your problems

3:06 fine and coming to the third type of graph but we don't concentrate this graph too much for your level that is acceleration time graph acceleration time graph okay so in short we can call it as at graph okay so we don't have much to study about this graph but definitely you need to focus these two graphs right so first and foremost let me quickly go for position time graph so i'm talking about xt graph right okay we all very well know that graph will always have two axis one is a vertical axis and the other one is

3:52 horizontal axis right see always time is taken as horizontal axis see we plot time in horizontal axis why only time is taken in horizontal axis y naught x it's because time is independent okay so it doesn't depend on anything so the independent variable is always taken in you know the horizontal axis right so in a vertical axis position is taken so x in the sense position here so position is taken in vertical axis and time is taken in horizontal axis right so and

4:38 for example imagine you have this information see uh this is the x and this is t say at time t is equal to zero seconds let me take time in seconds position in meters okay so when t is equal to zero your x is also equal to zero okay but at t is equal to one second imagine the object has moved two meters when t is equal to two seconds the object has moved four meters away when this is three seconds the object moved six meters when this is four seconds object moved eight meters when this is five seconds object moved ten meters say i gave you the information of position and

5:24 time so how do you mark the points on a graph so definitely you will take some scale right so this is your origin and let me take time as one second two second three second four second and five second that way and my uh you know the position as like one meter or two meter or let me take it as two meters four meters right six meters eight meters and so on so how do you mark right so you will mark the points so this is where when time is one the position is two meters so here you put a point and second point is here you will put like that looking at the information you will get certain

6:12 dots right and what you need to do all you need to do is you will have to join the dots isn't it so when you join the dots here in this case you are getting a straight line and you just check the information the object is moving equal distances in equal instance of time right say at one second it has moved two meters at two seconds it has moved four meters it has moved equal distance in equal interval of time so what is this motion called as definitely this is a uniform motion right so whenever an object follows uniform motion and for that object when you plot xt graph you will get a

6:58 straight line okay so this is a very very basic point that you need to remember right so uh the straight line the first point that i am writing here is if you get a straight line in xt graph okay then it indicates uniform motion it indicates uniform motion so this is a very very fundamental point one must understand okay fine very good so as long as the motion is uniform you know you will get uh you know a straight line and and what you can come to know through this straight line one thing i can say is uniform motion in the sense your velocity is constant

7:43 right so when velocity is constant what about the acceleration what is acceleration change in velocity when velocity is not changing acceleration a is acceleration a will be isn't it say this is what the fundamental points that you need to remember if you get a straight line acceleration is 0 in this case velocity is constant okay fine and another thing is so imagine i consider any two points right so this is one point i consider okay so let me call it as x one corresponding to this point uh you know the distance or the position is x one okay and

8:28 corresponding to this point you know the position is x two right and uh if i you know draw a line perpendicular to x-axis from this point and if i draw a line you know parallel to x-axis from this point both of them will meet here okay so what is this angle what is this angle this angle is nothing but tan theta right and what is this tan theta which is talking about slope right so slope of this line so what do you mean by slope so imagine guys this is your x-axis right and and you know the line looks something like this you see see how much

9:14 extinct this line is away from this t-axis so this is your t-axis and and and this is your slope you see here slope is nothing but this angle okay so the angle between this line and my t axis right so this angle becomes more and more when this line is away from t axis right so here the angle is very less but here the angle is more angle is more angle is more right so as the angle increases which is that this tan theta angle as it increases your slope will increase okay so this is actually imagine if this is this has to be on this and now this line is moving away away right so more the steepness of a line more is the slope this is what we

10:01 call it as a slope okay so this is what we will call it as slope so slope is nothing but tan theta right say uh the more the angle more will be the slope okay so what i can write more the angle more is the slope okay slope is nothing but how how steeper is the line okay so how much far the line is going away away from t axis so that is what we mean by slope and how do you calculate that slope say uh how do you calculate calculating slope is nothing but calculating tan theta calculating this angle so how do you calculate tan theta so we all know

10:47 tan theta is equal to it is opposite by adjacent right so opposite side opposite side is this adjacent side is this opposite by adjacent is what tan theta right and what is opposite so what is this distance what is this distance right say this is x 2 this is x 2 minus x 1 and what is this what is this if i this is the time interval right so let me call this as t2 and this as t1 okay so let me use the other chalk piece here this is t2 and this is t1 so t2 minus t1 is time

11:33 interval right so what is what is this distance what is this distance so just corresponding to this you have to check you will get to know right so what is x 2 8 right so x 2 minus x 1 by t 2 minus t 1 will give you tan theta so that is nothing but slope and theta is nothing but slope i mean to how much extent this line is away from t axis see that's what you're finding out by this angle theta right so uh slope is equal to this much so x2 is 8 8 minus x1 is 4 and t2 is how much 5 minus 3 right so it is 4 by 2

12:21 so that means your slope your slope is equal to 2 and and what is this actually this is nothing but displacement right see this is x2 minus x1 means what it is the distance between this point and this point so this is actually nothing but displacement right and this is nothing but time interval time interval right so you calculated displacement by time interval right so your slope is nothing but displacement by time interval

13:06 isn't it so what is displacement by time interval it is nothing but average velocity right so you calculated average velocity your slope value indicates the average velocity value that is 2 meter per second right so what is this 2 meter per second 2 meter per second is the average velocity it is the velocity difference between this point and this point okay so that's what we mean by slope so here the value of slope is nothing but the value of average velocity okay so another important point is

13:51 value of average velocity sign is this right value of average velocity can be found from slope can be found from slope okay so you can find out average velocity like this so between any two points if you want to find the average velocity just you just draw these lines okay so if i want to find the average velocity between this point and this point so what you will do align from this align from this and this is the angle you're finding so how do you find that just opposite by adjacent this difference okay in the

14:37 uh you know y-axis and this difference on the t-axis you have to identify substitute here calculate and give the average velocity you have to understand one point here guys average color velocity was easily calculated by knowing a graph right so when you plot a straight line it indicates that it is uniform motion and where uh the velocity is constant and you know if you can find the slope of this line then that itself is the value of average velocity between any two points okay fine so now we got to know how to find average velocity now what about the instantaneous velocity so let's understand about finding instantaneous

15:24 velocity see first of all you must know what is the meaning of instantaneous velocity instantaneous velocity is nothing but velocity at an instant of time velocity at an instant of time so what do you mean by instant of time okay so just try to analyze how we found average velocity say average velocity is uh the velocity change between the two points right so it is the velocity between two points but uh and and it is the velocity between the time interval right so in two seconds of time uh what was that speed you know that's what we meant by average velocity

16:10 but here exactly at fourth second i want to know what is its velocity then that is called as average velocity okay so exactly at four the second what is the speed what is the velocity that is called as instantaneous velocity okay so here if uh you know x t graph is a straight line this is a very important point guys if xt graph is straight line okay if it is a straight line uh instantaneous velocity okay so i'll write it as instantaneous velocity as v instant instantaneous velocity is equal to average velocity only so this is really

16:56 the way you found average velocity now say for example i took these two points and and you know this is how i have done and i found the slope of this line slope is nothing but here tan theta so this difference divided by this difference will give you slopes value this value okay that means i'm not talking your slope is not a length slope is how steeper is the line see how much uh this line is how much far from t axis right so that is slope so that slope you can always find by this difference this difference divided by this difference okay so the way you found average velocity can be applied for finding instantaneous velocity also so this is one important

17:42 point uh that you need to remember but instead of this if it is a curve something like this then average velocity uh cannot be equal to the instantaneous velocity then you have a different method for finding average velocity and different method for finding instantaneous velocity so now we will discuss when do you get that curve instead of a straight line when you have a curve then how to find the slope uh that means how to find the average velocity and how to find the instantaneous velocity that's what we are going to discuss now okay see guys when you have this information on a board how do you plot x t graph you can try plotting x t graph for this information see when time okay let me just put the axis and this is a vertical

18:30 axis i'll show x and this is a horizontal axis and this is t axis right okay so this is 0 let me take time as 1 2 three four five six and so on and this as with a scale uh you know five meters right and this is 10 meters and this is 15 meters and this is 20 this is 25 and so on okay so now if i start plotting when time is 0 our distance is also 0 right so when time is 1 then the distance is 3 so here i'll put a point and then when time is 2 our distance is 9 so here i am putting a point right so when time is 3 the distance is

19:16 sorry and for 2 here the point should come and for 3 where should the point must come it's 16 right so 16 is somewhere here right so like that when i go on putting a point something like this i get right so if i have to join all these points from origin how do i join so this is how i join normally is this a straight line no right this is not a straight line and this is a curve so and you see the information you don't have equal distances in equal time time is yes it's it's one second gap but in that one second gap uh does the distance is same at every interval no right see equal distances are not covered in equal

20:04 time so what kind of motion it is definitely it is a non-uniform motion okay so this is non-uniform motion right so you get a curve what is the first point that i would like to write here is curve in xt graph is shown okay for for non-uniform motion okay non-uniform motion but okay so here velocity is not constant that's it velocity is not constant but acceleration is constant that you

20:49 need to remember guys so here a is constant actually you know it's very nice to say that uniformly accelerated body this is the xt graph for this is the xt graph for uniformly accelerated body okay then then this is a perfect name okay so here velocity is not constant velocity is not constant so this is a perfect way of telling okay fine see whenever you get a curve velocity is not constant

21:34 whenever you have a straight line velocity is constant so this is really very important so for a straight line a is 0 but for a curve a is constant here okay so a is constant here is that clear so this is the difference you must understand okay so we all know x t graph slope okay so this is the graph this curve itself we will call it as a graph right so x t graphs uh you know use is to find the velocity average velocity so if it was a straight line it's very easy to find average velocity but what if it is a curve how do you find average velocity see here

22:21 what do we do is say for example these are the two points and between these two points i need to find the average velocity so what i have to draw is i will draw a line connecting these two points okay and and this line is what we will call as secant right so all these are mathematical terms maybe you are aware of all this so for a curve when i select two points and joining the two points when i draw a straight line like this and this is called as a secant okay so slope of this secant will give you average velocity okay so what is average velocity here slope of secant

23:08 secant is the value of value value of average velocity so this is really very very important okay so slope of secant is average velocity right so that's how you will find the average velocity whenever you have a curve and now how do you find instantaneous velocity right say for example and uh say this is the point where i need to find instantaneous say exactly at a time three seconds i want to know what is uh you know the velocity then that velocity is what we call it as instantaneous velocity so for instantaneous velocity

23:55 we have to take a tangent okay so just corresponding to this point draw a tangent so slope of tangent right so slope of tangent tangent will give will give instantaneous velocity so this is the difference guys instantaneous velocity okay so this is really very important to understand so whenever you have a curve in x t graph average velocity is nothing but slope of secant how do you draw a secant connect the two points okay and how do you find uh the instantaneous velocity it's nothing but the tangent

24:41 okay so the tangent at a particular point will give you the value of instantaneous velocity right but drawing a tangent at a particular point and all this needs much more information and it is very quite complicated part so that's why usually instantaneous velocities we won't find through graphs right so it can be found by integral simplification or differential form okay so on using a certain mathematical applications like differentiation we can easily find instantaneous velocity all that i will tell you in some other video okay like when the concept comes i'll tell about instantaneous velocity and instantaneous acceleration okay but i'm

25:27 just giving an idea from a graph also you can find the instantaneous velocity that is this is how you can find them okay so uh this is what the information that you must know when when you have a curve in xd graph okay fine so now what i would like to tell you is in case okay so in case if you are graphing something like this x t graph if you have something like this what does this mean this means that velocity is constant no doubt velocity is constant why i'm telling as velocity constant because straight line you have okay but velocity

26:14 is decreasing velocity is decreasing here okay so here velocity is decreasing and here the slope is negative right so you will have if i join these two points right so you will actually have a negative slope isn't it so slope is negative slope is negative right because the velocity is decreasing velocity is negative right so slope is negative here fine and what about this situation in case if you your xt graph is something like this right what does that mean you see as the time changes the position of the

27:01 object has not changed okay say for example this is uh 10 this is 20 this is 30 and this is 40 right say time one second two second three second four second so time is increasing gradually but the object you see it is there in the same position 40 40 40 40 40 or all through the times so what does this indicate if an object is staying at the same position throughout the time it indicates that object is at rest object is at rest this is very very important guys so whenever you have a line parallel to t axis whenever you have a line

27:46 parallel to t axis it indicates that object is at rest okay so whenever you have a graph something like this it means that velocity is increasing slope is positive okay so you all know how to calculate a slope right so a slope is calculated a change in the position divided by time interval right between the two points so that's how you're finding slope it's nothing but a tan theta okay and whenever you have a line something like this it means that velocity is decreasing and you will have a negative slope and whenever you have a curve it indicates that velocity is not constant

28:33 okay it is for uniformly accelerated body okay so here how do you find the average velocity velocity the the most important uh use of x t graph is to find the average velocity slope of a line will give you average velocity if it's a curve slope of a secant is average velocity and if you want to find instantaneous velocity it is a tangent slope of a tangent is instantaneous velocity okay but if it is a straight line uh you know the way you found average velocity can be applied for finding instantaneous velocity also so here average velocity remains equal to instantaneous velocity

29:18 if you have a straight line it can be a positive slope or negative slope okay fine and when you have a line which is parallel to t axis it indicates that object is not in a motion it is completely at rest okay so this is what the summary of you know x t graph and this is the use of x d graphs now we will see certain questions that can be asked in xd graph so that you will have an idea how we have to apply this concept and when we have to apply this concept see the question guys they have given a graph this is a xt graph see graph to look at is very much scary right but you must know how to read a graph okay so you must understand object from where it is moving to where

30:05 and how it is moving okay so when you can carefully read the graph then finding answers for the question is really very easy so everything is there in reading a graph okay fine let's let's read a graph little later first try to understand the question see see the xt graph and calculate average velocity between time minus 2 to plus 3 okay so time minus 2 is here and plus 3 here so between this time interval between this time interval there is a change in position of object definitely so average velocity you need to find the second question average velocity

30:51 between c to g okay so let me mark this is point a and this is b position b and this is position c okay and then uh this can be position d this is e this is f and this is g okay so you have to find the average velocity between c to g c is here when the object is here from here when it has moved to here so in this gap you have to find the average velocity and next question average velocity between minus 1 to 0 minus 1 to 0 so in this instance what is

31:39 the average velocity that also you need to find okay and next is uh instantaneous velocity at 7.5 so here at this point exactly when the time is at 7.5 where is the point yes here so here you need to find instantaneous at this point you need to find instantaneous velocity and instantaneous velocity at the time 6 that means at this point even at this point also you have to find instantaneous velocity okay and now i'll help you out in reading a graph so how do you read this graph see actually object has started from here right and from here the velocity was

32:26 increased okay so uh with almost it's it's a light curve guys so from the negative velocity slowly velocity increased and it reached at this point and later velocity decreased so with the decreasing velocity it has come to this point again velocity is slightly increased okay increase here also increase and you see the object from e to f there is no change in the position okay so if you see point e it is corresponding to 5 meters if you see point f it is corresponding to 5 meters only right so this is the area where object has not moved it has taken a rest okay so here the object is a test and

33:14 now again with constant velocity you know with increasing velocity the object has moved to point g and then velocity decreased okay so maybe the object is moving in the opposite velocity decreased means what the direction has changed okay so let me show the graph here see object is here at point a okay and you know from point a you you can see velocity is increased right that means the object is moving in the same direction right so it has reached point b from point b velocity is decreased that means negative velocity that means it it has moved backwards it means that the object has taken u turn okay so it

33:59 reached point c again from point c it is moving uh you know what almost forward i mean right say automatically from b to c the velocity is negative from c to d the velocity is positive again the direction has changed that means again you took it it took from u-turn okay it took a u-turn and this is point d from point d uh you know uh it it has moved here this is e and here you know it took a rest it has not moved uh for a while right so uh let me take this has taken a rest okay so this is your f and again with the positive velocity it is moving in the sense it's

34:45 moving forward and again here the velocity is decreased it's a negative velocity right so that means uh from g it took a u-turn and it is coming backward so this is what the motion of an object so this is how you must able to read a graph okay so uh this can actually help you out in solving many problems so important thing is reading a graph here okay fine so now let us try to answer the questions that they have asked first one average velocity between time minus 2 to time 3 so where is minus 2 minus 2 is here right so plus 3 is here

35:32 so in this time interval what is the average velocity so at minus 2 object was at this position and that plus 3 object is at this position okay so if you join these two points you know it's a curved graph right so you can just put a line here this is what we call it as secant right so this is what we mean by secant okay so now if you uh draw a line you know vertically downwards and from here horizontal this is where it meets and this is the angle you need to find out tan theta right so actually what you are doing it is i'm i'm just

36:18 finding out the first question average velocity at the time minus 2 to 3 okay for this question i'm finding out and you know this difference divided by this difference so what is the difference here see here it is at see this is your uh you know initial velocity is 3 right x1 this is x1 this is x2 right and you know here corresponding to this this is t1 and corresponding to this and this is t2 isn't it so here what is this what is this gap actually it is uh final velocity minus initial velocity that is 5 minus 3

37:04 phi minus 3 divided by what is this time interval this time interval it is 3 minus of minus 1 right so what do you get 2 it is actually minus 1 guys okay so this is actually minus one yes we have done it from minus one only right it's actually minus one so three plus one that is four right so it is one zero two right so almost average velocity is around 0.5 meter per second so this is the answer for first question like this for every information you have to find something like this only right so now let's go for the second question

37:49 they asked you to find average velocity between the point c to g okay so where is c c is here okay where is g g is here right so a line from c to g right so what is the slope that you get so g is here and let me join say slope this is what you have to find so this difference divided by this difference you have to do so what is this difference what is this different and where is g it is at 7 right and where is c c is at 1

38:35 so 7 minus 1 right so 7 minus 1 divided by time gap is what c is at 0 g is at 7 right so here it is 7 minus 0 that is 7 right so you will get 6 by 7 meter per second is your answer right so now coming to the third question they ask you average velocity between the time minus 1 to 0 so where is minus 1 okay so here is minus 1 minus 1 to okay so minus 1 to 0 minus 1 is at b

39:24 0 is for the position c minus 1 to 0 means you have to find the displacement or average velocity between b and c points b is here c is here right so this is a straight line only so this is what the slope right so here this difference divided by this difference this difference this difference let me call it as the x this difference let me call it as t see guys actually this is the initial position of if you see b and c object has come from b point to c point isn't it so this is the initial position this is the final position so what you have to do you have to do final minus

40:10 initial final position is at one in the y uh this y-axis and initial position is at three in the y-axis so it is one minus three you have to do and what is the time what is the time this is the initial time this is the final time right so 0 minus of minus 1 so you will get minus 2 divided by 1 that is minus 2 meter per second you see your velocity value is negative what does this negative means the velocity decreases you see from b point to c point object object is taking a u turn it its direction is changed so

40:56 plus 2 minus so that is the importance of this sign sine will tell you whether it is a positive velocity or negative velocity so it's a negative velocity right negative velocity means actually the object has taken a u-turn here okay fine so next question guys find the instantaneous velocity at the time 7.5 so instantaneous velocity at time 7.5 right so very 7.5 yes 7.5 is here so at this point you want to find the velocity i told you whenever you have a straight line in xt graph instantaneous velocity can be calculated as average velocity so here if i ask you to calculate average velocity how do you calculate it is the

41:41 velocity between this and this point so this is how you will make right so this difference divided by this difference divided by this difference right so this is what the angle you are trying to find out so what is this difference so where is our c c is at 2 okay g is at 7 this is the initial position this is the final position right so final minus initial so 2 minus 2 minus 7 divided by what is the time gap time gap you see this is t1 this is t2 t2 is at 8 second t1 is at 7 seconds so 8 minus

42:28 7 it will be 1 so it is minus 5 by 1 right so this one is our minus 5 by 1 meter per second that is minus 5 meter per second so here also you see the velocity is negative that means the object is changing its direction okay so velocity is actually decreasing i mean it's not actually decreasing okay so it is here the direction is changed that is what the meaning okay so this is the initial velocity this is a final velocity right so initial final position velocity is something like this so it is negative value right so now what is the last question instantaneous velocity at the time 6

43:15 that means at this point you have to find instantaneous velocity and this is also a straight line here so just a slope of this line if you can find that will be your answer so find the slope of this line guys that means this difference here check it out divided by this difference okay so find out and let me know the answer in a comment box post the answer in comment box so that's all about uh the different models of questions that can be asked on xt graph okay so this is how you must know how to read the graph and you must know how to calculate the slopes when it is asked in between different points and between different times okay so okay guys video

44:01 has become too much lengthy uh i just wanted to cover vt graphs also here but since it has become too much lengthy i'm keeping this vt graphs for next video and do watch my next video for vt graphs really vt graphs has lots of information to know about and we can calculate many many things from v to graph and not only that how to convert you know x t graph into v t graph and v t graph into x d graph that is also a very very important concept and we will look at some questions based on that concept also so do watch my next video also that is the continuation of this video actually okay so uh do practice the more the questions you practice more

44:47 perfect you will become actually so first thing is you must able to read the graph very nicely okay and then you must understand where is the velocity going to be a positive and where it is going to be a negative see velocity positive means object is moving you know in a positive direction velocity negative means automatically uh when a velocity becomes negative it means that the object is going in the opposite direction you see here here the velocity positive automatically here the velocity has become negative that means here the direction of object only has changed okay so uh that is all about xt graphs and see you in my next video do watch that that's really going to be a very very

45:33 interesting video okay and share the videos with your friends also and do subscribe our channel to learn the concepts in the easiest way and in a detailed way thank you so much [Music]